BEGIN:VCALENDAR VERSION:2.0 PRODID:-// BEGIN:VTIMEZONE TZID:Europe/London BEGIN:DAYLIGHT TZOFFSETFROM:+0000 TZOFFSETTO:+0100 TZNAME:BST DTSTART:19700329T010000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0100 TZOFFSETTO:+0000 TZNAME:GMT DTSTART:19701025T020000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT CATEGORIES:Category Theory Seminar SUMMARY:Universes for category theory - Zhen Lin Low\, DPM MS DTSTART;TZID=Europe/London:20130507T141500 DTEND;TZID=Europe/London:20130507T151500 UID:TALK44715AT URL: DESCRIPTION:The Grothendieck-Verdier universe axiom asserts th at every set is a member of some set-theoretic uni verse U that is itself a set. One can then work wi th entities like the category of all U-sets or eve n the category of all locally U-small categories\, where U is an "arbitrary\nbut fixed" universe\, a ll without worrying about which set-theoretic oper ations one may legitimately apply to these entitie s.\nUnfortunately\, as soon as one allows the poss ibility of changing U\, one also has to face the f act that universal constructions such as limits or adjoints or Kan extensions could\, in principle\, depend on the parameter U. The purpose of this ta lk is to explain how one can\nprove that this is n ot the case\, at least in the case of adjoints for accessible functors between locally presentable c ategories (and hence\, limits and Kan extensions)\ , making explicit the idea that ``bounded''\nconst ructions should not depend on the choice of U. LOCATION:MR9\, Centre for Mathematical Sciences CONTACT:Julia Goedecke END:VEVENT END:VCALENDAR